What is the difference between 125v and 250v fuse?

They have different maximum voltage values which impacts what the work they are able to do. You can't apply a fuse whose maximum voltage value is less than the voltage of the application. For example, a 125V fuse can be replaced with a 250V fuse of equal amplitude while the voltage of the application is 250V or lower, but a a 250V fuse can't be replaced with a 125V fuse of equal amplitude if the voltage of the application exceeds 125V.